I also did a recording of the right channel when music is playing. I fiddled a bit with play/pause and with volume control. The popping at the end of the recording occurs when the volume is completley turned off. Here's the recording of the right channel playing music: R channel with music

The noise on the left channel isn't that bad, but the fast popping on right channel is quite audible. What could be the reason for this kind of noise? Defunct cap? Bad resistor? Bad soldering work?

I think it's worth mentioning that I'm powering the circuit with a universal power supply set at 12V. Could this be the reason?

It could be due to powersupply. Maybe try to power it with batteries, to test it.

Have you tried with different OP Amp?
I had some noise when I used OPA2134 in ground channel for my amp wich has ground channel with opamp&buffer combo.
Noise was present only with that specific op amp, and only on the ground channel, for unknown reason to me.

I built one a few days ago that had the exact same issues at first. The issue got better (wasn't completely fixed) when I moved components around a bit and did some resoldering (mine was a little more compact and thought I might have an issue with the leads on my resistors shorting to pins on the opamp) It completely fixed itself once I put in new 470uF caps. (tbh I did some resoldering then too and changed out the power wires so It may have been one of those) check reisistances between different pathways. Is it what would be expected? (note: if you take resistance of a path with a capacitor in it you should see the resistance steadily rise as the cap charges) Also, if you have not yet done this, clean the flux off the board. This has caused issues like this for me before as well.

I'm also happy to see someone finally use that type of patterned perfboard. I've been pointing people to it for years, but I don't think I've ever seen anyone actually show a picture of one using it.

Are you sure this noise isn't coming from the source, and the CMoy's stock 11x gain isn't just magnifying it for you to hear? I see a MacBook in the background; are you by chance doing these tests with the Mac audio out plugged into the amp's audio in?

A better test for "no sound" is to short the inputs to ground. This removes the possibly noisy computer audio output from the system. If that removes the clicky noise, you can ameliorate the problem by lowering the amp's gain. You can't actually fix it without something like an external audio DAC; i.e. replacing the computer's analog audio output stage.

Also, do the test away from RFI sources. If that solves it, you might fix it by putting the amp in a metal, grounded enclosure.

The tests were made via an iPod Video 5.5th gen with a quite decent audio cable so I kinda doubt that the problem is in the source itself.

I managed to refine the sound a bit. The problem was indeed in the power supply. I built a simple voltage regulating circuit and the annoying noise is now almost completley gone. There still is some, but it's way better than before :).

cool. do you mind posting the schematic for that here? I've become very interested in the CMoy recently and I'd like to see how you implemented this (I have a generic psu that I'd like to see if I can get clean enough to power the thing)